DESIGN WINDOW CALCULATIONS
FOR A CONSTANT Q' LITHIUM BLANKET
COMPARING LITHIUM AND SODIUM COOLANTS
P.Gierszewski
B.Mikic
N.Todreas
PFC/RR-79-15
FUSION TECHNOLOGY PROGRAM
Massachusetts Institute of Technology
Cambridge, MA 02139
August 1979
Design Window Calculations for a Constant g' Lithium Blanket
Comparing Lithium and Sodium Coolants
ABSTRACT
In previous work(',2), a design window approach has been applied
to a liquid metal cooled, stagnant lithium breeding blanket, where the
cooling tubes are spaced such that they all have the same heat flux per
unit length (constant q').
This report is partly supplemental in that it
is a detailed clarification of the equations and assumptions used, including several refinements.
However, it also includes documentation for a
revised version of the WINDOW code used to generate the design windows,
and (as an example of the usefulness of the design window approach) a
comparison of lithium cooling to sodium cooling of this blanket.
results confirm the desirability of lithium as a coolant.
The
iii
Table of Contents
Page
Abstract
ii
Table of Contents
Nomenclature
iii
iv
1. Introduction
2. Design Window Analysis
3.
Program WINDOW
3
11
4. Comparison of Lithium and Sodium Cooling
13
5. Conclusions
21
6.
23
References
Appendix A:
Source Listing of Program WINDOW
24
Appendix B:
Sample Output (Case 5)
28
iv
Nomenclature
a
-
radial half-width of region cooled by i th cooling tube (m)
azimuthal half-width of region cooled by ith cooling tube (m)
bB
-
magnetic field strength (T)
C
-
defined by Eqn. (10)
C
- specific heat of coolant (J/kg-0 C)
C1
- pumping power ration
DhDt
- header and cooling tube diameter (m)
f
- defined by Eqns. (23) and (24)
Fc
- allowance factor in pressure loss calculations
h
- heat transfer coefficient (W/m2 -oC)
kc,kLi ks
thermal conductivity of coolant, structure and lithium pool (W/m-OC)
L
- major on-axis circumference of reactor (m)
M
- blanket energy multiplication factor
n
- number of coolant tubes per header
N
- number of blanket modules (or headers) azimuthally
Nt
- total number of coolant tubes
Nu
- Nusselt number
APh'AEt
- header and total pressure loss (Pa)
q'
- heat load per uniit length (W/m)
01
2.
- first wall neutron energy loading (W/m
)
q"'(r)
- volumetric heat generation rate in blanket (W/m3
Q
- total power removed per blanket module (W)
Qtotal
- total power removed from all modules (W)
v
radial distance from first wall (m)-
r
-
Ri
- radial position of ith coolant tube (m)
Rw
- first wall radius (m)
Rwo
- reference first wall radius for neutronics calculations (m)
S
- coefficient in q"'(r)
Si
- fitted reference coefficient from neutronics calculations (m)
th~tt
- header tube and coolant tube thickness (m)
Tin
- inlet temperature ( C)
Tm
- maximum lithium pool temperature (0C)
ATc
- coolant temperature rise across blanket (0 C)
ATf
- film temperature drop (0C)
ATm
- temperature drop between coolant tube and maximum in pool (0C)
ATw
- wall temperature drop (0C)
Uh
- coolant velocity at inlet (m/s)
v
- fitted coefficient in q'''(r)
x
- axial length of coolant tubes (m)
z
- radial thickness of blanket (M)
'ac,
c, s
-
(1/p)
(1/m)
fraction of blanket volume occupied by coolant and structural
material (exclusive of header region)
- coolant viscosity (kg/m-s)
p
- coolant density (kg/m 3
ac'Ys
- electrical conductivity of coolant and structure (1/a-m)
Clh
ay
- hoop stress (Pa)
- structural material design yield stress limit (Pa)
Design Window Calculations for a Constant q' Lithium Blanket
Comparinq Lithium and Sodium Coolants
1. Introduction
An interesting fusion reactor coolant/breeding material combination
is liquid metal cooling with a stagnant lithium pool breeding region.
A
design methodology is developed to identify the constraints on a constant
q' blanket model (Figure 1).
Here, coolant tubes (running parallel to the
main toroidal field to minimize MHD pressure loss) are distributed to
match the volumetric heating rate.
Each tube receives the same heat input.
This design emphasizes fewer tubes and lower thermal stresses.
The design window approach is to take basic thermal-hydraulic,
structural and neutronic constraints, and use them to define limit lines
in design parameter space.
Here the length of the coolant tubes (x) and
the number of tubes per module header (n)
are used as the unspecified para-
meters that must be chosen consistent with the constraints and design objecti ves.
The limiting constraints in this blanket model are:
- maximum lithium pool temperature (vapor pressure becomes too large);
- maximum coolant temperature (limited by corrosion of-tube material);
- minimum coolant temperature (coolant must be liquid, and hot enough for
useful energy generation efficiency);
- maximum stress (primary membrane stresses must be less than the structural material yield strength);
- maximum neutron fluence (limited by materials damage);
- minimum tritium breeding ratio (reactor must be self-sustaining);
2
N
B
2
,stagnant Li
-
tube
-
header
n(
Xh
n
I
coolant
Figure I.
Constant q' Blanket Model
I1
coolant
3
- maximum number of cooling tubes (reliability decreases with complexity);
- maximum pumping power to heat removal ratio (economic limit);
- maximum header diameter (limited by space).
There is sufficient information available to choose values for
most of these constraints, irrespective of reactor parameters.
For example,
the maximum lithium pool temperature is about 900 0 C. This allows a margin
0
of safety from the boiling point (1300 C), and keeps the vapor pressure
low (less than 13 kPa) such that the blanket module need not be pressurized.
The maximum pool temperature and other such constraints are implicitly included in the design window calculations.
The remaining constraints, notably the maximum neutron fluence,
the maximum number of coolant tubes and the maximum header diameter, are
more susceptible to other design considerations not included here.
Accor-
dingly, these constraints are drawn as contours or limit lines, n = n(x),
in the n-x design parameter space, and bound the acceptable design window.
2. Design Window Analysis
In this analysis of the constant q' blanket, materials properties
are assumed known and temperature independent, some typical or reference
reactor parameters are used, and values of the constraints are taken as
given.
In addition, a fitted function is used to describe the volumetric
heating rate through the blanket.
The intent is to derive expressions for
n = n(x) based explicitly on the total number of coolant tubes (Nt), the
header diameter (Dh)
and the first wall neutron loading (q").
w
The first limit line n = n(x) follows easily from the expression
for the total number of coolant tubes,
-4
Nt = NnL/x
(
where N is the number of blanket modules (azimuthally), and L is the
major circumference on axis.
The remaining equations require considerably more work.
From
neutronics calculations, the volumetric heating rate q"'(r) is expressed
approximately as
q"'(r) = Sq"e-vr
(2)
where S and v are fitted coefficients, and r is the distance from the
first wall.
Since the calculations are nominally for some reference first
wall radius Rwo, Eqn. (2) must be generalized to handle other Rw.
Now for
the same wall loading and total blanket volume
q"' = q".27rR L/volume
w
(3)
w
while for the same wall loading and blanket thickness
2
q"' = q" 2TrRL/{r(R
w
w+z) -TR }L
In either case, q"' increases as R
q"'(r)
(4)
increases, so
!W- S q"e-vr
which strictly is only correct for constant blanket volume.
(5)
Note also
that while q"'(r) may be correct for any fraction of lithium coolant in
the blanket, the fitted coefficients will not be correct over a wide range
of coolant volume fraction for other liquid metals.
5
I Given this heat generation rate, determine the size and location
Consider an arbitrary value of n. The tubes must
of the coolant tubes.
be radially spaced such that the constant q' condition is met.
Since q"'
decreases with r, the tubes are spaced further apart at the outer blanket
In fact, the radial distance between tubes is
edge than near the plasma.
given by
1 Rw+R.
1
where
2a
(6)
Rw+Ri ev(R i-R1 )
2a. = 2a
is the radial width of the blanket volume "covered" by the cooling
tube at radius R. from the first wall.
It is in the region around the
outer tubes that the maximum blanket temperature occurs, and here
a
n
Dt
R
2 Rn+Rw
e-vDt/ 2 evRn
(7)
which assumes Dt (tube diameter) << 2Rw and, more significantly, that
a1 = R
= Dt/2.
This latter implies that the tubes are very closely
spaced (radially) near the first wall.
Now an = z - R
where z is the blanket thickness.
So by deter-
mining Dt from other considerations, Eqn. (7) can be solved for Rn'
Ideally, Dt comes from the following system of equations:
n
z = E 2a.
i=l
2a
D
R
Rw+R
R =
e-vDt/2 evRi
£ 2a.-a.
(8a)
(8b)
(8c)
6
But Dt is only needed in the calcula-
However, this is a complex problem.
is not a dominant factor.
tion of the maximum pool temperature, and there it
Accordingly, use an approximation (accurate for large n) to get reasonable
results.
Rearrange z = E 2a. = Z 2a(R.) to obtain,
z
z
(
2a(R)
(dR
0 2a(R)
Therefore, using Eqn. (6),
2
evDt/
Dt
n
_vz
vz
1-(l+vz)eR v
2
vDt/
Dt
(10)
c
v
where c is the expression in brackets.
Now Dt is expected to be small, so Eqn. (10) can be reduced to give
D
-
c/nv.
But for a little more accuracy, expand the exponential,
Dt(I - vDt/2)
-
c/nv.
Solving the quadratic in Dt and taking the correct
root
Dt
(1
(1-/1--2c/n)/v
Using this value of Dt, Eqn. (7) can be solved for Rn, which is needed in
calculating the maximum lithium pool temperature, Tmax*
In particular, the maximum temperature difference between the
lithium pool and the coolant is given by(l,2)
im=2
f 2(Rn) (
Li
D2a(b_
) +r
(b
b n n 2a n(12)
t
7
where
bn =
(this assumes
-vDt/2
Rwe
Dt
anRw+Rn
vRn
r(Rw+Rn )/N
bn > an
-
otherwise simply interchange their definitions).
This can be written as
ATm = q". f
(13)
w
where f is a function of known quantities.
The maximum blanket temperature is Tmax, where
Tm
For given Ti
=T
+ ATc + ATf + ATW + ATm
(14)
and ATc (coolant temperature rise), and ATm from Eqn. (13),
only the film (ATf) and wall (ATw) temperature drop need be found.
The
wall temperature drop is easily obtained as
AT
Nu k
2t
) AT
-2
k ln(l+
where tt and ATf are still undetermined.
(15)
(Under the blanket conditions,
Nu is approximately constant over a wide range of flow velocities.)
The total power absorbed (and extracted) from each blanket module
can be expressed in terms of the coolant temperature rise,
D2
Q = U
pc AT
(16)
or in terms of the heat transfer rate to the coolant,
Q = n hATf xITDt = n Nu kCATf
Xr(
8
or in .terms of the pumping power to heat removal ratio C,
Q = APt Puh
D2
4
c
(18)
or in terms of the absorbed energy flux
Q
q"(r) x 2f_ (Rw+r) dr
0
N
Here Uh is the coolant velocity in the headers, and APt is the total pressure drop.
Using Eqn. (5), Eqn. (19) becomes
NQ = q" 2TRwxM
(20)
S
=wovz
{1+Rwv-(w+vz+R v)e-v
(21)
where M is the effective blanket energy multiplication factor since
q" 2rrR x is the incident neutron power.
(It is assumed that the first
wall thermal load is removed by a separate cooling system.)
Returning to the film temperature drop, combine Eqns. (17) and
(20) to obtain
AT
=
q" 2RWM / Nn Nu kc
(22)
Since Tmax is a known constant, Eqns. (13), (14), (15) and (22) can be
rearranged to yield
Tmax - Tin - ATc
q =_
w
2Rw M -i+ Nu kc ln(+
tt)
+f(23)
nN Nu knc
kNs
12
Dt
The ratio tt Dt comes from the hoop stress limit, which is (because liquid
metal coolants operate at low pressure)
9
Dt
Y(24)
Ap
t
h-y
and from combining Eqns. (16) and (18) to give
EPt
Gpc ATC
(25)
So Eqn. (23) gives the second limit line in terms of the wall loading.
It is independent of x because the temperature constraints can be met
for arbitrary x by suitable flow rates.
This brings up the final limit line which, by using a maximum
hoop stress and a header diameter limit, restricts the maximum possible
flow rate.
In particular, it relates the maximum flow velocity to the
maximum pumping power ratio through the pressure drop.
A general expression for the total pressure drop would include
(1) MHD pressure loss in the header where flow is perpendicular to the
B field, (2) friction pressure loss, (3) MHD pressure loss at corners,
and (4) MHD losses through regions of changing B field.
Simple satis-
factory solutions are available for the first two terms, but not for the
rest.
Fortunately, usually only the-first term is significant. For the
purposes of this analysis, total pressure drop is taken as the MHD pressure loss in the header region multiplied by an allowance factor,
FC
AP
= Fc A
(26)
This factor is intended to encompass all other pressure loss terms and
can be improved as better models become available.
From calculations
for several typical cases, Fc = 1.6 was found to be conservative.)
10
An approximate expression
for the header pressure drop, valid
for large Hartmann number flow (H=B(Dt/2) /ac/u ) is
2 tac
H2 4
AP
h ~ 1
-
DO
2TthOc
(Dh/h2 )2 ztotal
(27)
Dh s
where Oh is the average header velocity and ztotal is the total header
length (blanket plus shield).
The blanket inlet header velocity Uh is
of particular interest since it determines the total coolant mass flow,
and here it is assumed that Uh - Oh, which is correct if the header is
tapered towards the first wall.
It is also assumed that the blanket and
shield are of comparable thickness so that ztotal
2z.
For the same maximum hoop stress in headers and coolant tubes,
and allowing the pressure--and hoop stress-- to be equal everywhere if
a tube becomes blocked, then
Dh/th = Dt/tt
(28)
Equations (24) to (28) can be rearranged to yield the maximum
header velocity consistent with
Gh 5 Oy
u
uhmax
-
[
Clpc pAT c +y_9
a.-c
a
s
(7r/8)
F
c B2
(29)
where allowance has been made for pressure drop in the two headers.
At this maximum velocity, a restriction on the header diameter
would give a maximum flow rate
pUhmax
straight, then the maximum Dh is
.-
Dh.
If the header is
11
(30)
Dh < 2rrRW/N
but if it tapers in towards the first wall,
Dh
<
(31)
27(Rw+z)/N
where the diameter of the headers is restricted at the entrance to the
blanket module.
The maximum amount of energy that can be removed is then given
Combining this with Eqns. (20) and (23) then the third
by Eqn. (16).
limit line is
1+
2RWMQ
n
where
1
n
=
.
ln(l+ -2tt
Dt
2 ks
Nu kc '{2nRwMx (Tmax-T in-
Q = L'hsmax
-Dh2 . pc
ATc
So Eqns. (1), (23) and (32) are of the form
the limit lines for the design window.
into a program
WINDOW
(32)
) - fNQ
n = n(x)
and describe
These equations are incorporated
(described in the next section) and are applied
to lithium and sodium coolants in the final section.
3. Program WINDOW
The design window analysis has been implemented in the computer
program WINDOW.
In particular, WINDOW solves the limit line
n = n(x)
from Eqn. (32), and in the p-rocess yields values for the other two limit
lines given by Eqns. (1) and (23).
interestinq design variables such as
It also calculates and prints other
ATf.
12
The program is a short FORTRAN program, with the input specifically put on cards in the deck itself.
The data needed includes materials
data, reactor parameters, limiting parameters and fitted coefficients for
q"'(r).
These are listed (along with typical values) in the next section.
A source listing of the program is enclosed, which indicates exactly how
the data if formatted.
The output consists of a list of reactor parameters evaluated at
the limit line from Eqn. (32) -- the Dh limit line -- at a range of values
of n. Plotting n versus x gives this limit line.
Since q" = q"(n) only,
and since q"(n) values are output, then the second set of limit lines
can also be drawn.
Nt limit line.
The final set is obtained easily from Eqn. (1) -- the
A typical output is enclosed.
The input variables are explained in the program.
The output
variables are:
N
- number of coolant tubes per blanket module (or header);
- header inlet velocity;
DELTAP - total pressure drop through blanket;
UH
DT
- coolant tube diameter;
TT
- coolant tube thickness;
- distance of last coolant tube from first wall;
- temperature difference between last coolant tube and
maximum temperature in lithium pool;
- film temperature drop at last coolant tube's exit;
RN
TM
TF
TW
QW
QTOT
X
- wall temperature drop at last coolant tube's exit;
- first wall neutron loading;
- total reactor thermal power;
- length of blanket module (without headers);
ALPHAS - percentage of structure in blanket volume, assuming
straight headers;
ALPHAC - percentage of coolant in blanket volume, assuming straight header
NT
- total number of coolant tubes in reactor.
13
4. Comparison of Lithium and Sodium Cooling
Liquid metals such as lithium and sodium are good, low pressure,
high temperature, radiation damage resistant blanket coolants.
Lithium
is of special interest because it also moderates neutrons and breeds
tritium, has low induced activity, and is quite compatible with the refractory metals.
There is still interest, however, in liquid sodium as a near-
term reactor coolant, especially in fusion-fission hybrids (5,6).
because there is more experience with sodium (i.e.,
This is
the LMFGR program),
it is less corrosive to Fe and Ai based alloys (and stainless steel is the
most likely near-term structural material), it is cheaper than lithium, it
(3)
is inert to tritium, and it is somewhat less reactive
This section compares the two liquid metals as heat transfer
agents.
The purpose is to further quantify the relative merits of these
coolants and to illustrate the design window methodology just developed.
Table 1 lists the parameters examined in this report, and compares
them with representative values from some roughly comparable detailed
reactor studies.
Table 2 lists the materials properties used.
While
changing these parameters (e.g. TZM rather than stainless steel structure,
or N = 20 rather than 100) will quantitatively change the conclusions, it
is not believed that this will substantially affect the qualitative conclusions regarding lithium versus sodium coolant.
The volumetric heat generation rate is taken as
q"'I(r) = 4.67 (
:
)
e-4.256r
(r, Rw in m)(
n,
ri(rium
y3 li . ) qtpool/
T i s r t 4.6
(33)
This is strictly only true for lithium pool/lithium cool ant, but is assumed
14
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4)
4W
o
0
Cn
-C
-C
vn
> 4. '- 0
4J
C
dI
4
tv
a)-
In
r-
u u
4-)
2
41
*
-34U1 -r-
a)
C*
ro
0)
0g
4.
4.
In
0
S---
o
4--o
-C
4.)
ej
0
0-
4
C
0
-0-
o
C
0.
.-C4.)
F--
M
-0-
.r-
Co
o
.
o
A-
I--
4r-
-) -
LL
V)
r
'16
reasonable for small volume fractions of sodium coolant (in the examples
shown here, there is typically about 6% coolant, 0.5% structure).
Further-
more, since the pure lithium case had a breeding ratio of about 1.4,0)
the small amount of sodium coolant should not reduce the breeding unacceptably low.
Figures 1, 2 and 3 show the design windows for lithium and sodium
coolant.
200
0 C,
Figure 1 uses identical reactor parameters (notably
900 0 C).
Tmax =
for Nt < 10000,
Ti
=
ATc
=
The shaded area is the acceptable design window
Dh < 0.251 m and
q" > 1.0 1W/m 2.
Figure 2b takes ad-
vantage of the possible higher operating temperature of sodium /steel as
compared with lithium/steel).
Only the Dh limit line is appreciably
changed, and two cases of T. = 230 0 C, AT c = 300 0 C and
ATC = 200 0 C are shown.
T. = 300 0 C,
Figure 2a is identical with Figure la and is
repeated to simplify comparison of the lithium and sodium curves.
Figure 3
again uses identical reactor parameters, but Trmax is dropped to 600 0 C and
Nt reduced to 5000, to represent near-term reactor objectives.
Table 3
compares the blanket parameters at point A--the maximum first wall loading
design consistent with the constraints (note, though, that n is an integer,
so some leeway was taken with the Nt line).
From all results, it is quite clear that lithium is a better coolant
than sodium.
Not only does it lead to larger option spaces, but it allows
higher wall loading operation, higher total thermal power, and even fewer
tubes for operating at a given wall loading.
The higher possible tempera-
ture of the sodium/steel system allows the optimum sodium design to approach
the optimum cooler lithium/steel system (Case 3 compared with Case 1) but is
17
Figure 1.
Design windows for lithium and sodium coolants. Tin=200 0 C
T
=900 0 C
max
N < 10000
t
q">1.0 MW/m
w
2
0
ATc=2000 C
h<25. 1 cm.
2
Nt=1 000 0
Nt=5000
q"=4.0 MW/m
20 ----------------- -------- --------------------------- -------------------18.
16
A
(a) Lithium coolant
S14,
I-
-c 10
4-)
q"=2.0 Kd/m 2
6
q"=1.0 r-:d1m
4J
'4-
E
D
2
0
0
20
Tube length, x
h
2 5 .1 cm
30
(m)
N t=10000
N =5000
-q2=4.0 MW/r
2
18
S16-
(b)
Sodium coolant
14
o,1210
-
q"=2.0
2
MA/m
q"1.
W
A/
42
'4-
068 ------40
0
--
--- ----- ------------------------- ------------------
EW
Dh =25 .1 cm
00
0
1. 0
Tube length, x
20
(m)
3o
18
Figure 2.
Design windows for lithium and sodium, where the sodium coolant is allowed
to be 100 C higher at exit than the lithium coolant.
Nt=10000
4.0
Nt=5o06
N~
~=4.o
Nt
20
'----------------- -----------------20 -----------------
l 2
--- RA/m 2
-------------q
18
6
(a) Lithium coolant
A
14
0
~l2
q"=2.0 Kd/m 2
.10,
0
8
6.
4 ----- -----
Sq"1=1.0
--------------------------------------------------------
t-7/m2
---2 =2 5 .1 cm
T. =200 0 C AT =2000C
10
20
'
Tube length, x
(m)
Nt=5000
Nt=10000
20
30
q"=3.0 MW/rm 2
18
16A
14
3
(b)Sodium coolant
0
q"=2.0 MW/m 2
S12A
S10
J
4
T30
'4-T=20
o8.i
.0
4-
10
20
Tube length, x
30
(m)
19
Figure 3.
20 1
(a)
0
0
Design windows for lithium and sodium. Tin=200in
C, AT c=200
C, Tmax =600 0 C
C
Lithium coolant
2
Nt=5 00
Nt=10000
18
A5
2
16
0
0
-
14
w"=1.0MW/m
12 i----- ----.---- -------------- ------------------------------ -------- -----10
D h=25.1 cm
8
q"=0.5 MWd/m2
6
4
2'
0*0
20
10
Tube lenath, x
20
(m)
Nt= 1000 0
(b) Sodium coolant
Nt= 50 00
18
1-
30
q"=1.5 MW/m
2
16
14
0
--
12
A
2
q"=1 .0 HW/m
10
0
81
q"=0. 5MW/m
Dh= 2 5 .1 cm
4
2
U0
2
10
20
Tube length, x (m)
30
20
Table 3:
Comparison of Lithium and Sodium Coolants
for Maximum q" Design
Parameter
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Figure
la
lb
2b
2b
3a
3b
Coolant
Li
Na
Na
Na
Li
Na
Tiin(0 C)
200
200
200
300
200
200
AT C(C)
200
200
300
200
200
200
900
900
900
900
600
600
10300
10500
10300
10500
5100
5000
q" (MW/m2 )
3.3
2.6
2.6
2.2
1.4
1.1
Qtotal (MW)
n
678
16
353
11
503
15
334
12
678
18
353
x(m)
9.4
6.3
8.8
7.0
21.
15.
uh(m/s)
0.32
0.31
0.31
0.31
0.32
0.31
APt (MPa)
4.3
2.3
3.2
2.2
4.3
2.3
Dt(cm)
1.6
2.4
1.7
2.2
1.6
2.2
tt(cm)
ATm (C)
0.058
427
0.045
452
0.046
356
0.040
360
0.058
171
0.042
181
ATf(0 C)
45.
31.
26.
28.
18.
12.
AT w(C)
27.
16.
17.
12.
11.
aS()
0.86
0.66
0.69
0.58
0.48
0.38
ac(
6.0
8.7
6.4
8.0
3.3
4.9
Tmax
(0 C)
Nt
12
6.6
21
So while sodium is still a viable coolant--all con-
still -not superior.
straints considered here can be met--these results show that lithium
coolant is definitely the thermal-hydraulic choice.
These results confirm the conclusion that could be drawn directly
from the -materials properties (Table 2) themselves.
For liquid metal coolants
in magnetic fields, two rough figures of merit are PC
and a. The first is
a measure of the coolant's ability to absorb heat, and the second is a
measure of the resistance to flow in a magnetic field.
should be large and the second small.
(PCp)Na =
l.1x106 J/m3- 0 C,
and
Ideally, the first
At 300 0 C, (PCP)Li = 2.2x106 J/rm-
aLi =3.3x10' (Q-m) 1 ,
Clearly lithium is superior in both respects.
0C ,
a = 5.7xl06 (2-m)-
The results of this design
window analysis illustrate exactly how these material advantages affect the
blanket design.
5.
Conclusions
The analysis in this report clarifies and refines the analysis of
a liquid metal cooled, stagnant lithium breeding blanket with constant q'
coolant tube spacing using a general design window methodology.
In parti-
cular, expressions are obtained relating basic reactor parameters to constraint curves in
n-x
space, for the particular constraints of maximum
number of coolant tubes (reliability limit), first wall neutron load
(design objective) and header diameter (physical geometry limit).
A com-
puter program, WINDOW, to calculate the design window curves is documented.
This analysis is then applied to a general comparison of lithium
and sodium coolants.
The results confirm that lithium is a better heat
22
transfer agent (3.3 MW/m 2 maximum first wall loading as compared with
2.6 MW/m 2 , for the best cases considered here), although sodium is still
shown to meet the basic constraints considered here.
This application also
serves to illustrate the usefulness of the design window approach.
23
6. References
1.
J. Chao, B. Mikic and N. Todreas, "Thermal-Hydraulic and Neutronic
Considerations for Designing a Lithium-cooled Tokamak Blanket,"
PFC/RR-79-ll, MIT, 1979.
2.
J. Chao, B. Mikic and N. Todreas, "A Parametric Study of a Lithium
Cooled Tokamak Blanket," Nud.. Tech., 42, January 1979, p. 22.
3.
B. Badger et al., "UVMAK-I, A Wisconsin Toroidal Fusion Reactor Design,"
UWFDM-68, University of Wisconsin, Vol. I, 1974, p. IV-A-3.
4.
M. Hoffman and G. Carlson, "Calculational Techniques for Estimating the
Pressure Losses for Conducting Fluid Flows in Magnetic Fields,"
UCRL-51010, Lawrence Radiation Laboratory.
5.
"Proceedings of the Second Fusion-Fission Energy Systems Review Meeting,
Vol. I, November 1977," CONF-771155, DOE, July 1978, p. 149.
6.
G. Moses, R. Conn and S. Abdel-Khalik, "Laser Fusion Hybrids - Technical,
Economic and Proliferation Considerations," UUFDM-273, University
of Wisconsin, November 1978.
7.
B. Gore and E, Murphy, "Current Fusion Power Plant Design Concepts,"
BNWL-2013, Battelle Pacific Northwest Laboratories, September 1976.
8.
B. Badger et al., "UNMAK-III, A Non-circular Tokamak Power Reactor
Design," EPRI ER-368, Vol. I, July 1976.
9.
R, Werner, "ORNL Fusion Power Demonstration Study: The Concept of the
Cassette Blanket," ORNL/TM-5964, Oak Ridge National Laboratory,
October 1977.
10,
D. Rigney, S. Kapelner and R. Cleary, "The Electrical Resistivity of
Lithium and Columbium-1 Zirconium Alloy to 1430 0 C," Pratt and
Whitney Aircraft (CANEL), TIM-854 (1965).
11,
J. Ballif et al., "Lithium Literature Review:
Interactions," HEDL TC-1000 (1978).
12.
G. Holden and J. Tokor, "Thermophysical Properties of Sodium," ANL-7323,
Argonne National Laboratory, August 1967.
13.
"Nuclear System Materials Handbook, Vol. 1, Design Data," TID-26666,
Book 1, Hanford Engineering Development Laboratory, revised to
June 15, 1979.
Lithium's Properties and
24
Appendix A
Source listing of program WINDOW
25
Le
L
of
Z
n
I
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al
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~ ~j- ~.j-
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<
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<-
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%
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=
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c:
J. .J.J 21
1
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C
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+
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4
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~~~~
j
tf
=
7 11 11
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t
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4
mC
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I - -4
%
1
U 11
OL
-
1
f
1 1 Z 11
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=
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Z
01 11.
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I
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,
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t.
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0 . 0
0~ "'
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-
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)
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(.
en
0
3
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.. ~ 0
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000
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z- +
0
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-17
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**j*
...
11
t ItN1 i
Z
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+
0-r0
J-L
;
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Q
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z
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e
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0
~
<
o
4
.
0~0Li
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Oe~0O
000000
c 0
C7
r4
27
-4
U-
x
I
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r
-
4
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o
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4.
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2-
0
UJ
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- 4.
*
I
z
a.
0
CP
9
0
r
28
Appendix B
Sample output of program WINDOW
This output is for Case 5 of Table 3.
29
-.
co
'r
X
N r
N
N 4-
en
4
.'v
t -
r.
w
-N
~ ~ ~ a.~ ~.'a.F r--
tQ 0C
LU
.0
U"
N
'
0 ON C-
NC
1N0.p
-
4na
4
2:
0
-4
C,
0- Ln'
M C.
-
N
w4-
I'-
.0
4
CC
2:
U'
en- I. "
-4
en~. f
en en a'n rn
<
0
y2
0nZ
o
400
-4
0J
U.
N N'
Li.
-j
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Z--4
.4 )4
2'
. %AL-
2:_j~~J0
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LU
If zb
VI
*2
nO~
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~ ~--
- -
-
LA.
0
--
- 0r
.-
- 0- 0 - a- ..
fn